Super-wide angle optical systems such as fisheye lenses and omnidirectional mirrors can project an image with an angle of view of 180 degrees or more, onto a single image plane, and is used in various areas in which a wide photographic field of view is required.
In an image obtained toy photography using a super-wide angle optical system, the shapes of the captured objects appear distorted by barrel distortion, in comparison with an image of a normal perspective projection, so that the captured image (distorted image) gives an odd impression if it is displayed without alteration. Therefore, when a video obtained using a super-wide angle optical system is displayed, a region of interest, which is a part of the image, is extracted, and the extracted image is transformed to an image of a normal perspective projection method, before the display.
In this transformation, a projection surface (a projection sphere) on a hemispherical surface on one side of the image plane is assumed, and a projection is made from the projection sphere to the image plane. This projection includes a process of determining the position on the image plane corresponding to a point of interest on the projection sphere. Patent Reference 1 shows use of the zenith angle for the computation of the image height (distance from the optical axis) on the image plane, in this process (column 7). If the zenith angle is used, it is necessary to determine a trigonometric function of the zenith angle, when, for example, the projection is performed by orthographic projection, stereographic projection, or equisolid angle projection. Patent Reference 1 discloses the use of a lookup table for simplifying the process of determining the trigonometric function.